WASHINGTON (AP) _ Republican Donald Trump and Democrat Hillary Clinton took major steps toward claiming their parties' presidential nominations with sweeping wins on Super Tuesday, the biggest day in the primary campaign.

Clinton and Trump each won seven states, as the front-runners padded their leads in the all-important delegate counts that determine the parties' nominees.  Though state primaries and caucuses will continue for months, rivals will be hard-pressed to catch up with the front-runners.

That increases the likelihood of a Trump-Clinton showdown in the November election, offering voters what would likely be the starkest contrast in presidential candidates they have seen in their lifetimes.  It would pit Clinton, the politically cautious, detailed-oriented former secretary of state and senator, against Trump, the trash-talking political outsider who has generated outrage with his derogatory comments about Muslims, Mexicans and women, among others, yet has won over many Americans angry at Washington and anxious about terrorism, immigration and the economy. 
 
Clinton turned away from rival Bernie Sanders and set her sights on Trump as she addressed supporters during a victory rally in Miami.

"It's clear tonight that the stakes in this election have never been higher and the rhetoric we're hearing on the other side has never been lower,'' said Clinton, who is trying to become America's first female president. President Barack Obama is barred by the constitution from seeking re-election after two four-year terms.

Trump, too, had his eye on a match-up with Clinton, casting her as part of a political establishment that has failed Americans.
 
"She's been there for so long,'' Trump told a news conference at his swanky Mar-a-Lago resort in Florida. "If she hasn't straightened it out by now, she's not going to straighten it out in the next four years.''
 
Trump's dominance has rattled Republican leaders, who fear the billionaire real estate mogul and former reality TV star is unelectable against Clinton in November. But Tuesday's results did little to clarify which of two senators _ Ted Cruz or Marco Rubio _ might emerge as Trump's main Republican rival, with both vowing to fight on despite weak performances.
 
Cruz, a firebrand conservative senator, won the biggest prize, his home state of Texas, and neighboring Oklahoma, as well as Alaska, giving him four wins overall, including the leadoff Iowa caucuses. But Cruz failed elsewhere in the South, which was considered prime territory for him, watching as Trump displayed surprising strength with evangelical Christians and social conservatives. .
 
Still, Cruz called on Rubio and other candidates to step aside.
 
"I ask you to prayerfully consider our coming together, united,'' Cruz said.
 
Rubio emerged Tuesday with his first victory, in the Minnesota caucuses, but did not live up to the wider hopes of the numerous Republican officeholders who have promoted him as the party's best alternative to Trump. His hopes are now on the March 15 primary in his home state of Florida, where, unlike Tuesday's contests, the winner will claim all the delegates. 
 
In the Democratic race, Clinton has faced a tougher-than-expected challenge from Bernie Sanders, a Vermont senator and self-described democratic socialist who has energized supporters with his calls for a "political revolution'' and denunciations of America's wealth gap. But Sanders has struggled to expand his base beyond young people and liberals. 
 
Sanders won four states Tuesday _ Colorado, Minnesota, Oklahoma and his home state of Vermont. But Clinton won the biggest states and by wide margins, giving her a much larger share of delegates.
 
Clinton was assured of winning at least 457 of the 865 delegates at stake on Super Tuesday, while Sanders picked up at least 286 delegates. Overall, Clinton now has at least 1,005 delegates. Sanders had at least 373. It takes 2,383 delegates to win the nomination.
 
Clinton won in Texas, Massachusetts, Arkansas, Alabama, Tennessee, Georgia and Virginia. The wins reflected her strength in the South, where black voters are an important part of the Democratic base. Clinton also won in the South Pacific island chain of American Samoa.  Clinton was supported by at least 80 percent of black voters in the Deep South and Texas. She was also bolstered by women and older voters. 

Trump won in Virginia, Arkansas, Alabama, Massachusetts, Tennessee, Vermont and Georgia. 
 
Trump won 203 delegates Tuesday, while Cruz picked up 144. Overall, Trump leads the field with 285 delegates, with 1,237 needed for the nomination. Cruz has 161, Rubio has 87, Ohio Gov. John Kasich has 25 and retired neurosurgeon Ben Carson has eight.
 
Both Cruz and Rubio have launched furious verbal attacks on Trump in recent days, but some in the party establishment fear the anti-Trump campaign has come too late.
 
Republicans spent months largely letting Trump go unchallenged, wrongly assuming that his populist appeal with voters would fizzle. Instead, he's appeared to only grow stronger, winning states and drawing support for some of his most controversial proposals.
 
In six of the states voting Tuesday, large majorities of Republican voters said they supported a proposal to temporarily ban all non-citizen Muslims from entering the United States, an idea championed by Trump. The exit polls were conducted by Edison Research for The Associated Press and television networks.